I’ve been working hard this year to encourage students to document their understanding as they gain it, to use conscientious note-taking to create a resource for themselves as they go through the course. This means asking them repeatedly, “What could we write down about this that might be important for the future?” and getting some very blank stares.
It’s a task that’s very difficult for the students, and understandably so. Solving a specific problem correctly, or writing down a corrected solution that someone else has solved, involves much different thinking than extrapolating from that example what big ideas are actually at play. But I’m convinced that there’s a lot to gain by encouraging students to work on it time and time again.
Following a practice sheet on displacement, designed to encourage students to see how positive and negative signs can indicate the direction that the object has moved, I devoted 20 minutes of class time to discussing “big ideas” that could be recorded in the Consensus Notebook. At the end of that time (which consisted of both small group and whole class discussion), we’d come to consensus on one tiny thing – that displacement of an object is the same regardless of where on the object position was measured. Whew!!
For homework, I asked students to email to me a sentence or two describing something else that we might write in “CVPM 3 and CVPM 4”. My hope was that this would give them more time to mull over what might be a good contribution, and the results have been mixed. But read the first response to the vectors section – it’s exquisite!!
CVPM 4: Vectors: Values That Have Direction
• There is no one direction for positive or negative. The direction of the positive and the negative numbers are defined by the direction you determine. This is because if we had a normal horizontal, left to right number line the direction of negative would be left and the direction of positive would be right. However, if we were to change the way in which the number line was orientated then this would no longer apply, for example, if we made the number line move vertically the direction for negative would be down.
• If there is any displacemnent at all, then there is movement…so when you are thinking about a negative displacment dont think of it as negative movement because there still is movement
• Be careful when graphing positive and negative displacment, because they go in different directions
• You can decide if something is positive or negative only if the directions are determined for you (either by someone else or yourself).
CVPM 3: Displacement
• displacement- the change in position from the initial value to the final value
• If your initial value is negative, then in your equation it is going to be positive. ( two negatives equal a positive)
• If your initial value is negative, when you do the equation to find the displacement value, you must make it positive because you cannot subtract a negative value.
• If your initial is greater than your final and your initial is a negative, then the outcome of the equation will be positve.
• Displacement can be positive or negitive. It all depends on which way you define positive direction and negitive direction. When you don’t have initial and final placement you can try to compare and contrast the different points to surrounding objects and items.
• Based off whether or not our “Delta X” is positive/negative, we can tell if the object moved further away or closer to the reference point.
• Positive displacement is moving towards the positive side of zero
• Negative displacement is moving towards the negative side of zero
• Displacment deals with the separation points between point A and B in which the object is moving to and from, it doesnt have anything do with its path it takes to go there
• It is important to keep in mind which direction the number line/tape measure is going in order to always know which way is positive and which way is negative. If the number line is rotated differently each time the direction it wouldn’t stay constant, for example on a negative position we assume it always goes left but it could go down, right, etc. By being aware of the direction of a number line you can determine the correct change in position or displacement instead of misinterpreting it.
• When finding the delta or displacment from an object, the X initial’s position should always be measured the same way as the X final. However, the delta or displacement will always be the same if measured from the front, middle, back, etc.
##consensus ##cvpm ##practice